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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// =========================================================================================</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// KXG363 - Advanced Games Programming</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">// =========================================================================================</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Author: Robert Ollington</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Quaternion.h</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Quaternion class - all implementation is in the header</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef QUATERNION_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define QUATERNION_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor"></span>    </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;Vector3.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#include &quot;Matrix3x3.h&quot;</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;Matrix4x4.h&quot;</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;Math.h&quot;</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">namespace </span>T3D {</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;</div>
<div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html">   29</a></span>&#160;    <span class="keyword">class </span><a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    {</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="keyword">public</span>:</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keyword">union </span>{</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;            <span class="keyword">struct </span>{</div>
<div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">   34</a></span>&#160;                <span class="keywordtype">float</span>    <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>; </div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">   35</a></span>&#160;                <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>; </div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;            };</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;            <span class="keyword">struct </span>{ <span class="keywordtype">float</span> elem[4]; }; </div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;        };</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;</div>
<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">   42</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>() {<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>=1; <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a> = <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a>(0,0,0); }</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#ad5abd09be466be4b0ac66e6d1eb953bb">   50</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html#ad5abd09be466be4b0ac66e6d1eb953bb">Quaternion</a>(<span class="keywordtype">float</span> real, <span class="keywordtype">float</span> x, <span class="keywordtype">float</span> y, <span class="keywordtype">float</span> z): <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>(real), <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>(x,y,z) {}</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;</div>
<div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a7286f9b4e59fee5c8020958b4e0e3035">   56</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html#a7286f9b4e59fee5c8020958b4e0e3035">Quaternion</a>(<span class="keywordtype">float</span> real, <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> &amp;i): <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>(real), <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>(i) {}</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;</div>
<div class="line"><a name="l00063"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a137438607cb89c9d9bace3bbf81047f6">   63</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html#a137438607cb89c9d9bace3bbf81047f6">Quaternion</a>(<span class="keywordtype">float</span> theta_x, <span class="keywordtype">float</span> theta_y, <span class="keywordtype">float</span> theta_z)</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        {</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;            <span class="keywordtype">float</span> cos_z_2 = cosf(0.5f*theta_z);</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            <span class="keywordtype">float</span> cos_y_2 = cosf(0.5f*theta_y);</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            <span class="keywordtype">float</span> cos_x_2 = cosf(0.5f*theta_x);</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;            <span class="keywordtype">float</span> sin_z_2 = sinf(0.5f*theta_z);</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;            <span class="keywordtype">float</span> sin_y_2 = sinf(0.5f*theta_y);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            <span class="keywordtype">float</span> sin_x_2 = sinf(0.5f*theta_x);</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            <span class="comment">// and now compute Quaternion</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>   = cos_z_2*cos_y_2*cos_x_2 + sin_z_2*sin_y_2*sin_x_2;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x = cos_z_2*cos_y_2*sin_x_2 - sin_z_2*sin_y_2*cos_x_2;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y = cos_z_2*sin_y_2*cos_x_2 + sin_z_2*cos_y_2*sin_x_2;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z = sin_z_2*cos_y_2*cos_x_2 - cos_z_2*sin_y_2*sin_x_2;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        }</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    </div>
<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a91789d9f59d876e82b24c92605a56bdb">   83</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html#a91789d9f59d876e82b24c92605a56bdb">Quaternion</a>(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> &amp;angles)</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;        {   </div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;            <span class="keywordtype">float</span> cos_z_2 = cosf(0.5f*angles.z);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;            <span class="keywordtype">float</span> cos_y_2 = cosf(0.5f*angles.y);</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            <span class="keywordtype">float</span> cos_x_2 = cosf(0.5f*angles.x);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;            <span class="keywordtype">float</span> sin_z_2 = sinf(0.5f*angles.z);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;            <span class="keywordtype">float</span> sin_y_2 = sinf(0.5f*angles.y);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;            <span class="keywordtype">float</span> sin_x_2 = sinf(0.5f*angles.x);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <span class="comment">// and now compute Quaternion</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>   = cos_z_2*cos_y_2*cos_x_2 + sin_z_2*sin_y_2*sin_x_2;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x = cos_z_2*cos_y_2*sin_x_2 - sin_z_2*sin_y_2*cos_x_2;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y = cos_z_2*sin_y_2*cos_x_2 + sin_z_2*cos_y_2*sin_x_2;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z = sin_z_2*cos_y_2*cos_x_2 - cos_z_2*sin_y_2*sin_x_2;        </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;        } </div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;</div>
<div class="line"><a name="l00103"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a34d83a6ed93f0e1831850ca1cee9a663">  103</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html#a34d83a6ed93f0e1831850ca1cee9a663">Quaternion</a>(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_matrix3x3.html">Matrix3x3</a> &amp;m)</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        {   </div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;            <span class="keywordtype">float</span> t = m[0][0]+m[1][1]+m[2][2];</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;            <span class="keywordtype">float</span> r = sqrt(1+t);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a> = 0.5f*r;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x = 0.5f*sqrt(1+m[0][0]-m[1][1]-m[2][2]); </div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;            <span class="keywordflow">if</span> ((<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x&gt;0 &amp;&amp; m[2][1]-m[1][2]&lt;0) || (<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x&lt;0 &amp;&amp; m[2][1]-m[1][2]&gt;0)) <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x = -<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y = 0.5f*sqrt(1-m[0][0]+m[1][1]-m[2][2]); </div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            <span class="keywordflow">if</span> ((<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y&gt;0 &amp;&amp; m[0][2]-m[2][0]&lt;0) || (<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y&lt;0 &amp;&amp; m[0][2]-m[2][0]&gt;0)) <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y = -<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z = 0.5f*sqrt(1-m[0][0]-m[1][1]+m[2][2]); </div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;            <span class="keywordflow">if</span> ((<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z&gt;0 &amp;&amp; m[1][0]-m[0][1]&lt;0) || (<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z&lt;0 &amp;&amp; m[1][0]-m[0][1]&gt;0)) <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z = -<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        } </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        </div>
<div class="line"><a name="l00117"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a2ac79860a274ec8f8fe42a767e27fc9c">  117</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;<a class="code" href="class_t3_d_1_1_quaternion.html#a2ac79860a274ec8f8fe42a767e27fc9c">operator =</a>(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q)     </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        { <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>= q.<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>; <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>= q.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>; <span class="keywordflow">return</span> *<span class="keyword">this</span>; }</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> operator +(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q)<span class="keyword"> const  </span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>+q.<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>, <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>+q.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>); }</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> operator -(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;q)<span class="keyword"> const  </span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>-q.s, <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>-q.v); }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> operator *(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;q)<span class="keyword"> const  </span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="keyword">        </span>{   <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.s - <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.<a class="code" href="class_t3_d_1_1_vector3.html#aea3be73fc8042f2bd19f81672f70945b">dot</a>(q.v),</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                      <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*q.v.z - <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z*q.v.y + <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.v.x + <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*q.s,</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                      <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z*q.v.x - <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*q.v.z + <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.v.y + <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*q.s,</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                      <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*q.v.y - <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*q.v.x + <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.v.z + <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z*q.s);</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> operator /(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;q)<span class="keyword"> const  </span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="keyword">        </span>{</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> p(q); </div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;            p.invert(); </div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span> * p;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        }</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> operator *(<span class="keywordtype">float</span> scale)<span class="keyword"> const</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*scale,<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>*scale); }</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> operator /(<span class="keywordtype">float</span> scale)<span class="keyword"> const</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>/scale,<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>/scale); }</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> operator -()<span class="keyword"> const</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>(-<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>, -<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>); }</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;operator +=(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;q)      </div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        { <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>+=q.v; <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>+=q.s; <span class="keywordflow">return</span> *<span class="keyword">this</span>; }</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;operator -=(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;q)      </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        { <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>-=q.v; <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>-=q.s; <span class="keywordflow">return</span> *<span class="keyword">this</span>; }</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;operator *=(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;q)      </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        {           </div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;            <span class="keywordtype">float</span> x= <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x, y= <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y, z= <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z, sn= <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.s - <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.<a class="code" href="class_t3_d_1_1_vector3.html#aea3be73fc8042f2bd19f81672f70945b">dot</a>(q.v);</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x= y*q.v.z - z*q.v.y + <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.v.x + x*q.s;</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y= z*q.v.x - x*q.v.z + <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.v.y + y*q.s;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z= x*q.v.y - y*q.v.x + <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q.v.z + z*q.s;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>= sn;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;            <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;        }</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;operator *= (<span class="keywordtype">float</span> scale)         </div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;        { <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>*=scale; <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*=scale; <span class="keywordflow">return</span> *<span class="keyword">this</span>; }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;        <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a> &amp;operator /= (<span class="keywordtype">float</span> scale)         </div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        { <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>/=scale; <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>/=scale; <span class="keywordflow">return</span> *<span class="keyword">this</span>; }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    </div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;</div>
<div class="line"><a name="l00175"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a1900cc9df98213dd4b5df574a5fd8887">  175</a></span>&#160;        <span class="keywordtype">float</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a1900cc9df98213dd4b5df574a5fd8887">length</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span> (<span class="keywordtype">float</span>)sqrt(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a> + <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.<a class="code" href="class_t3_d_1_1_vector3.html#aea3be73fc8042f2bd19f81672f70945b">dot</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>)); }</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div>
<div class="line"><a name="l00182"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a8a4ab822e725b00342ae07b7079bf6b3">  182</a></span>&#160;        <span class="keywordtype">float</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a8a4ab822e725b00342ae07b7079bf6b3">squaredLength</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span> (<span class="keywordtype">float</span>)(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a> + <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.<a class="code" href="class_t3_d_1_1_vector3.html#aea3be73fc8042f2bd19f81672f70945b">dot</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>)); }</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;</div>
<div class="line"><a name="l00186"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a2e076399228a48deb6f469483978dfec">  186</a></span>&#160;        <span class="keywordtype">void</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a2e076399228a48deb6f469483978dfec">normalise</a>()</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;        { *<span class="keyword">this</span>/=<a class="code" href="class_t3_d_1_1_quaternion.html#a1900cc9df98213dd4b5df574a5fd8887">length</a>(); }</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;</div>
<div class="line"><a name="l00192"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#ab5488299b2ad47fdb67b20fe46b65666">  192</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> <a class="code" href="class_t3_d_1_1_quaternion.html#ab5488299b2ad47fdb67b20fe46b65666">normalised</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="keyword">        </span>{ <span class="keywordflow">return</span>  *<span class="keyword">this</span>/<a class="code" href="class_t3_d_1_1_quaternion.html#a1900cc9df98213dd4b5df574a5fd8887">length</a>(); }</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;</div>
<div class="line"><a name="l00196"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#aa22423bdf63803cff2071f3f4d0fc589">  196</a></span>&#160;        <span class="keywordtype">void</span> <a class="code" href="class_t3_d_1_1_quaternion.html#aa22423bdf63803cff2071f3f4d0fc589">conjugate</a>()</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;        { <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>=-<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>; }</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;</div>
<div class="line"><a name="l00200"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a1fd7bf3a7e3e6f03b4f867a98038634a">  200</a></span>&#160;        <span class="keywordtype">void</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a1fd7bf3a7e3e6f03b4f867a98038634a">invert</a>()</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;        { <a class="code" href="class_t3_d_1_1_quaternion.html#aa22423bdf63803cff2071f3f4d0fc589">conjugate</a>(); *<span class="keyword">this</span>/=<a class="code" href="class_t3_d_1_1_quaternion.html#a8a4ab822e725b00342ae07b7079bf6b3">squaredLength</a>(); }</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    </div>
<div class="line"><a name="l00207"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a15193f0c7b6344c850355fcd252010bd">  207</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> <a class="code" href="class_t3_d_1_1_quaternion.html#a15193f0c7b6344c850355fcd252010bd">log</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;<span class="keyword">        </span>{</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;            <span class="keywordtype">float</span> a = (float)acos(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>);</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;            <span class="keywordtype">float</span> sina = (float)sin(a);</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> ret;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;            ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a> = 0.f;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;            <span class="keywordflow">if</span> (sina &gt; 0.f)</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;            {</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x = a*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x/sina;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y = a*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y/sina;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z = a*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z/sina;</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x= ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y= ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z= 0.f;</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;            }</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;            <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;        }</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;</div>
<div class="line"><a name="l00229"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a61eaf3b0493547b96702789d214c62be">  229</a></span>&#160;        <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> <a class="code" href="class_t3_d_1_1_quaternion.html#a61eaf3b0493547b96702789d214c62be">exp</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="keyword">        </span>{</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;            <span class="keywordtype">float</span> a = (float)<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.<a class="code" href="class_t3_d_1_1_vector3.html#a65c1d2dc44afb8cf90e4762a3287f6c0">length</a>();</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;            <span class="keywordtype">float</span> sina = (float)sin(a);</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;            <span class="keywordtype">float</span> cosa = (float)cos(a);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> ret;</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;            ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a> = cosa;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;            <span class="keywordflow">if</span> (a &gt; 0.f)</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;            {</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x = sina * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x / a;</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y = sina * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y / a;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z = sina * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z / a;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;                ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x = ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y = ret.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z = 0.f;</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;            }</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;            <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;        }</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;</div>
<div class="line"><a name="l00249"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a19aabb06f5f967b1ca2391bb917a3a3d">  249</a></span>&#160;        <span class="keyword">operator</span> <a class="code" href="class_t3_d_1_1_matrix4x4.html">Matrix4x4</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;<span class="keyword">        </span>{           </div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;            <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_matrix4x4.html">Matrix4x4</a>(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>,  -<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x, -<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y,-<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z,</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;                    <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x,  <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>,  -<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z, <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y,</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;                    <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y, <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z,    <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>,-<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x,</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;                    <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z,-<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y,  <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x,   <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>);</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;        }</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    </div>
<div class="line"><a name="l00258"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a7a86bc98c962c5cee6984eb5c131bfe3">  258</a></span>&#160;        <span class="keyword">operator</span> <a class="code" href="class_t3_d_1_1_matrix3x3.html">Matrix3x3</a>() </div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;        {</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;            <span class="keywordflow">if</span> (fabs(<a class="code" href="class_t3_d_1_1_quaternion.html#a8a4ab822e725b00342ae07b7079bf6b3">squaredLength</a>()-1.0f)&gt;0.0001f){</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;                <a class="code" href="class_t3_d_1_1_quaternion.html#a2e076399228a48deb6f469483978dfec">normalise</a>();</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;            }</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;            <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_matrix3x3.html">Matrix3x3</a>(1-2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y+<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z), 2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y-<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z),   2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z+<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y),   </div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;                    2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y+<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z),   1-2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x+<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z), 2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z-<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x),   </div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;                    2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z-<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y),   2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z+<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x),   1-2*(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x+<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y));</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        }</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;</div>
<div class="line"><a name="l00273"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#ac5132ebdc6f63be990ac30626ea84edb">  273</a></span>&#160;        <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="class_t3_d_1_1_quaternion.html#ac5132ebdc6f63be990ac30626ea84edb">dot</a>(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q1, <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q2) </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;        { <span class="keywordflow">return</span> q1.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.<a class="code" href="class_t3_d_1_1_vector3.html#aea3be73fc8042f2bd19f81672f70945b">dot</a>(q2.<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>) + q1.<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*q2.<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>; }</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;</div>
<div class="line"><a name="l00282"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a027156cbbcbace6bf41525d9e7f34350">  282</a></span>&#160;        <span class="keyword">static</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> <a class="code" href="class_t3_d_1_1_quaternion.html#a027156cbbcbace6bf41525d9e7f34350">lerp</a>(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q1, <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q2, <span class="keywordtype">float</span> t) </div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;        { <span class="keywordflow">return</span> (q1*(1-t) + q2*t).<a class="code" href="class_t3_d_1_1_quaternion.html#ab5488299b2ad47fdb67b20fe46b65666">normalised</a>(); }</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;</div>
<div class="line"><a name="l00293"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#ad73ecf570146978e1811f60fa63374b3">  293</a></span>&#160;        <span class="keyword">static</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> <a class="code" href="class_t3_d_1_1_quaternion.html#ad73ecf570146978e1811f60fa63374b3">slerp</a>(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q1, <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> &amp;q2, <span class="keywordtype">float</span> t) </div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;        {</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> q3;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;            <span class="keywordtype">float</span> <a class="code" href="class_t3_d_1_1_quaternion.html#ac5132ebdc6f63be990ac30626ea84edb">dot</a> = <a class="code" href="class_t3_d_1_1_quaternion.html#ac5132ebdc6f63be990ac30626ea84edb">Quaternion::dot</a>(q1, q2);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;            <span class="comment">/*  dot = cos(theta)</span></div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="comment">                if (dot &lt; 0), q1 and q2 are more than 90 degrees apart,</span></div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;<span class="comment">                so we can invert one to reduce spinning */</span></div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;            <span class="keywordflow">if</span> (dot &lt; 0)</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;            {</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;                dot = -<a class="code" href="class_t3_d_1_1_quaternion.html#ac5132ebdc6f63be990ac30626ea84edb">dot</a>;</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;                q3 = -q2;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;            } <span class="keywordflow">else</span> q3 = q2;</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;        </div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;            <span class="keywordflow">if</span> (dot &lt; 0.95f)</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;            {</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;                <span class="keywordtype">float</span> angle = acosf(dot);</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;                <span class="keywordflow">return</span> (q1*sinf(angle*(1-t)) + q3*sinf(angle*t))/sinf(angle);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;            } <span class="keywordflow">else</span> <span class="comment">// if the angle is small, use linear interpolation                               </span></div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;                <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a027156cbbcbace6bf41525d9e7f34350">lerp</a>(q1,q3,t);       </div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;        }</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;</div>
<div class="line"><a name="l00321"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#afb8195aec8da40cb3f71f0f8eb67a2b3">  321</a></span>&#160;        <span class="keyword">static</span> <span class="keyword">inline</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> <a class="code" href="class_t3_d_1_1_quaternion.html#afb8195aec8da40cb3f71f0f8eb67a2b3">fromAngleAxis</a>(<span class="keywordtype">float</span> angle, <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> &amp;axis)</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;        { <span class="keywordflow">return</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">Quaternion</a>(cosf(angle/2), axis*sinf(angle/2)); }</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;</div>
<div class="line"><a name="l00328"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a9a41fcf96f67e9c89f0d2800e05a936c">  328</a></span>&#160;        <span class="keywordtype">void</span> <a class="code" href="class_t3_d_1_1_quaternion.html#a9a41fcf96f67e9c89f0d2800e05a936c">toAngleAxis</a>(<span class="keywordtype">float</span> &amp;angle, <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> &amp;axis) </div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;        {</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;            <span class="keywordflow">if</span> (<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>&gt;1) <a class="code" href="class_t3_d_1_1_quaternion.html#a2e076399228a48deb6f469483978dfec">normalise</a>();</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;            angle = 2.0f*acosf(<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>);</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;            <span class="keywordtype">float</span> k = sqrt(1-<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;            <span class="keywordflow">if</span> (k&lt;0.0001){</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;                axis.x = 0; axis.y = 0; axis.z = 1;</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;                axis.x = <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x/k;</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;                axis.y = <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y/k;</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;                axis.z = <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z/k;</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;            }</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;        }</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;</div>
<div class="line"><a name="l00344"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a5901e1f6605a90d37ad3dc20babf3958">  344</a></span>&#160;        <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> <a class="code" href="class_t3_d_1_1_quaternion.html#a5901e1f6605a90d37ad3dc20babf3958">rotate</a>(<span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> &amp;<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>)</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;        {   </div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> V(0, v);</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;            <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a> <a class="code" href="class_t3_d_1_1_quaternion.html#aa22423bdf63803cff2071f3f4d0fc589">conjugate</a>(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;            conjugate.<a class="code" href="class_t3_d_1_1_quaternion.html#aa22423bdf63803cff2071f3f4d0fc589">conjugate</a>();</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;            <span class="keywordflow">return</span> (*<span class="keyword">this</span> * V * conjugate).v;</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;        }</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;</div>
<div class="line"><a name="l00355"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#aeca5d04f00eae931e1b35a6c3c8e1f35">  355</a></span>&#160;        <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> <a class="code" href="class_t3_d_1_1_quaternion.html#aeca5d04f00eae931e1b35a6c3c8e1f35">eulerAngles</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;<span class="keyword">        </span>{</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;            <span class="keywordtype">float</span> sqw = <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>*<a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>;    </div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;            <span class="keywordtype">float</span> sqx = <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x;    </div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;            <span class="keywordtype">float</span> sqy = <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y;    </div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;            <span class="keywordtype">float</span> sqz = <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z*<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z;    </div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;            </div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;            <span class="keywordtype">float</span> unit = sqx + sqy + sqz + sqw;</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;            <span class="keywordtype">float</span> test = <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y + <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z * <a class="code" href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">s</a>;</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;            <a class="code" href="class_t3_d_1_1_vector3.html">Vector3</a> euler;</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;            <span class="keywordflow">if</span> (test &gt; 0.4999f * unit) <span class="comment">// Singularity at north pole                       </span></div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;            {               </div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;                euler.y = 2.f * (float)atan2f(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x, s);  <span class="comment">// Yaw</span></div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;                euler.z = Math::PI * 0.5f;              <span class="comment">// Roll</span></div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;                euler.x = 0.f;                          <span class="comment">// Pitch</span></div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;                <span class="keywordflow">return</span> euler;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;            }</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (test &lt; -0.4999f * unit) <span class="comment">// Singularity at south pole                     </span></div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;            {</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;                euler.y = -2.f * (float)atan2f(<a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x, s); <span class="comment">// Yaw</span></div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;                euler.z = -Math::PI * 0.5f;             <span class="comment">// Roll</span></div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;                euler.x = 0.f;                          <span class="comment">// Pitch</span></div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;                <span class="keywordflow">return</span> euler;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;            }</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;            <span class="keywordflow">else</span></div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;            {</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;                euler.y = (float)atan2f(2.f * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y * s - 2.f * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z, sqx - sqy - sqz + sqw);       <span class="comment">// Yaw</span></div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;                euler.z = (float)asinf(2.f * test / unit);                                             <span class="comment">// Roll</span></div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;                euler.x = (float)atan2f(2.f * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.x * s - 2.f * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.y * <a class="code" href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">v</a>.z, -sqx + sqy - sqz + sqw);      <span class="comment">// Pitch</span></div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;            } </div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;            <span class="keywordflow">return</span> euler;</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;        }</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;        <span class="keyword">inline</span> <span class="keyword">friend</span> std::ostream&amp; <span class="keyword">operator</span> &lt;&lt;</div>
<div class="line"><a name="l00392"></a><span class="lineno"><a class="line" href="class_t3_d_1_1_quaternion.html#a60829c0f8f2a36602ab5fdbb1a79b635">  392</a></span>&#160;            ( std::ostream&amp; o, <span class="keyword">const</span> <a class="code" href="class_t3_d_1_1_quaternion.html">Quaternion</a>&amp; q )</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;        {</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;            o &lt;&lt; <span class="stringliteral">&quot;Quat(&quot;</span> &lt;&lt; q.s &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; q.v.x &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; q.v.y &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt; q.v.z &lt;&lt; <span class="stringliteral">&quot;)&quot;</span>;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;            <span class="keywordflow">return</span> o;</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;        }</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    };</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;}</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;<span class="preprocessor">#endif </span></div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;<span class="preprocessor"></span></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_ad5abd09be466be4b0ac66e6d1eb953bb"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#ad5abd09be466be4b0ac66e6d1eb953bb">T3D::Quaternion::Quaternion</a></div><div class="ttdeci">Quaternion(float real, float x, float y, float z)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:50</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a7286f9b4e59fee5c8020958b4e0e3035"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a7286f9b4e59fee5c8020958b4e0e3035">T3D::Quaternion::Quaternion</a></div><div class="ttdeci">Quaternion(float real, const Vector3 &amp;i)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:56</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a2e076399228a48deb6f469483978dfec"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a2e076399228a48deb6f469483978dfec">T3D::Quaternion::normalise</a></div><div class="ttdeci">void normalise()</div><div class="ttdoc">normalizes this Quaternion </div><div class="ttdef"><b>Definition:</b> Quaternion.h:186</div></div>
<div class="ttc" id="class_t3_d_1_1_matrix3x3_html"><div class="ttname"><a href="class_t3_d_1_1_matrix3x3.html">T3D::Matrix3x3</a></div><div class="ttdef"><b>Definition:</b> Matrix3x3.h:22</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a9a41fcf96f67e9c89f0d2800e05a936c"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a9a41fcf96f67e9c89f0d2800e05a936c">T3D::Quaternion::toAngleAxis</a></div><div class="ttdeci">void toAngleAxis(float &amp;angle, Vector3 &amp;axis)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:328</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_aeca5d04f00eae931e1b35a6c3c8e1f35"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#aeca5d04f00eae931e1b35a6c3c8e1f35">T3D::Quaternion::eulerAngles</a></div><div class="ttdeci">Vector3 eulerAngles() const </div><div class="ttdef"><b>Definition:</b> Quaternion.h:355</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a027156cbbcbace6bf41525d9e7f34350"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a027156cbbcbace6bf41525d9e7f34350">T3D::Quaternion::lerp</a></div><div class="ttdeci">static Quaternion lerp(const Quaternion &amp;q1, const Quaternion &amp;q2, float t)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:282</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_ab5488299b2ad47fdb67b20fe46b65666"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#ab5488299b2ad47fdb67b20fe46b65666">T3D::Quaternion::normalised</a></div><div class="ttdeci">Quaternion normalised() const </div><div class="ttdef"><b>Definition:</b> Quaternion.h:192</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a5cca6c63059d5dc4206092fabdf67740"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a5cca6c63059d5dc4206092fabdf67740">T3D::Quaternion::s</a></div><div class="ttdeci">float s</div><div class="ttdoc">the real component </div><div class="ttdef"><b>Definition:</b> Quaternion.h:34</div></div>
<div class="ttc" id="class_t3_d_1_1_vector3_html_aea3be73fc8042f2bd19f81672f70945b"><div class="ttname"><a href="class_t3_d_1_1_vector3.html#aea3be73fc8042f2bd19f81672f70945b">T3D::Vector3::dot</a></div><div class="ttdeci">float dot(const Vector3 &amp;other) const </div><div class="ttdef"><b>Definition:</b> Vector3.h:278</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a5901e1f6605a90d37ad3dc20babf3958"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a5901e1f6605a90d37ad3dc20babf3958">T3D::Quaternion::rotate</a></div><div class="ttdeci">Vector3 rotate(const Vector3 &amp;v)</div><div class="ttdoc">rotates v by this Quaternion (Quaternion must be unit) </div><div class="ttdef"><b>Definition:</b> Quaternion.h:344</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a519e11430740c46525537c626e2002ce"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a519e11430740c46525537c626e2002ce">T3D::Quaternion::v</a></div><div class="ttdeci">Vector3 v</div><div class="ttdoc">the imaginary components </div><div class="ttdef"><b>Definition:</b> Quaternion.h:35</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a61eaf3b0493547b96702789d214c62be"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a61eaf3b0493547b96702789d214c62be">T3D::Quaternion::exp</a></div><div class="ttdeci">Quaternion exp() const </div><div class="ttdef"><b>Definition:</b> Quaternion.h:229</div></div>
<div class="ttc" id="class_t3_d_1_1_vector3_html"><div class="ttname"><a href="class_t3_d_1_1_vector3.html">T3D::Vector3</a></div><div class="ttdef"><b>Definition:</b> Vector3.h:22</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_ad73ecf570146978e1811f60fa63374b3"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#ad73ecf570146978e1811f60fa63374b3">T3D::Quaternion::slerp</a></div><div class="ttdeci">static Quaternion slerp(const Quaternion &amp;q1, const Quaternion &amp;q2, float t)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:293</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a91789d9f59d876e82b24c92605a56bdb"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a91789d9f59d876e82b24c92605a56bdb">T3D::Quaternion::Quaternion</a></div><div class="ttdeci">Quaternion(const Vector3 &amp;angles)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:83</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a15193f0c7b6344c850355fcd252010bd"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a15193f0c7b6344c850355fcd252010bd">T3D::Quaternion::log</a></div><div class="ttdeci">Quaternion log() const </div><div class="ttdef"><b>Definition:</b> Quaternion.h:207</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a2ac79860a274ec8f8fe42a767e27fc9c"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a2ac79860a274ec8f8fe42a767e27fc9c">T3D::Quaternion::operator=</a></div><div class="ttdeci">Quaternion &amp; operator=(const Quaternion &amp;q)</div><div class="ttdoc">basic operations </div><div class="ttdef"><b>Definition:</b> Quaternion.h:117</div></div>
<div class="ttc" id="class_t3_d_1_1_vector3_html_a65c1d2dc44afb8cf90e4762a3287f6c0"><div class="ttname"><a href="class_t3_d_1_1_vector3.html#a65c1d2dc44afb8cf90e4762a3287f6c0">T3D::Vector3::length</a></div><div class="ttdeci">float length() const </div><div class="ttdef"><b>Definition:</b> Vector3.h:217</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a8a4ab822e725b00342ae07b7079bf6b3"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a8a4ab822e725b00342ae07b7079bf6b3">T3D::Quaternion::squaredLength</a></div><div class="ttdeci">float squaredLength() const </div><div class="ttdef"><b>Definition:</b> Quaternion.h:182</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a1fd7bf3a7e3e6f03b4f867a98038634a"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a1fd7bf3a7e3e6f03b4f867a98038634a">T3D::Quaternion::invert</a></div><div class="ttdeci">void invert()</div><div class="ttdoc">inverts this Quaternion </div><div class="ttdef"><b>Definition:</b> Quaternion.h:200</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a1900cc9df98213dd4b5df574a5fd8887"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a1900cc9df98213dd4b5df574a5fd8887">T3D::Quaternion::length</a></div><div class="ttdeci">float length() const </div><div class="ttdef"><b>Definition:</b> Quaternion.h:175</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_aa22423bdf63803cff2071f3f4d0fc589"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#aa22423bdf63803cff2071f3f4d0fc589">T3D::Quaternion::conjugate</a></div><div class="ttdeci">void conjugate()</div><div class="ttdoc">computes the conjugate of this Quaternion </div><div class="ttdef"><b>Definition:</b> Quaternion.h:196</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a019944a146d7d35841d6a567abed5f49"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a019944a146d7d35841d6a567abed5f49">T3D::Quaternion::Quaternion</a></div><div class="ttdeci">Quaternion()</div><div class="ttdef"><b>Definition:</b> Quaternion.h:42</div></div>
<div class="ttc" id="class_t3_d_1_1_matrix4x4_html"><div class="ttname"><a href="class_t3_d_1_1_matrix4x4.html">T3D::Matrix4x4</a></div><div class="ttdef"><b>Definition:</b> Matrix4x4.h:24</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_afb8195aec8da40cb3f71f0f8eb67a2b3"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#afb8195aec8da40cb3f71f0f8eb67a2b3">T3D::Quaternion::fromAngleAxis</a></div><div class="ttdeci">static Quaternion fromAngleAxis(float angle, const Vector3 &amp;axis)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:321</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a137438607cb89c9d9bace3bbf81047f6"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a137438607cb89c9d9bace3bbf81047f6">T3D::Quaternion::Quaternion</a></div><div class="ttdeci">Quaternion(float theta_x, float theta_y, float theta_z)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:63</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_a34d83a6ed93f0e1831850ca1cee9a663"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#a34d83a6ed93f0e1831850ca1cee9a663">T3D::Quaternion::Quaternion</a></div><div class="ttdeci">Quaternion(const Matrix3x3 &amp;m)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:103</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html">T3D::Quaternion</a></div><div class="ttdoc">A quaternion class adapted from http://willperone.net/Code/Quaternion.php. </div><div class="ttdef"><b>Definition:</b> Quaternion.h:29</div></div>
<div class="ttc" id="class_t3_d_1_1_quaternion_html_ac5132ebdc6f63be990ac30626ea84edb"><div class="ttname"><a href="class_t3_d_1_1_quaternion.html#ac5132ebdc6f63be990ac30626ea84edb">T3D::Quaternion::dot</a></div><div class="ttdeci">static float dot(const Quaternion &amp;q1, const Quaternion &amp;q2)</div><div class="ttdef"><b>Definition:</b> Quaternion.h:273</div></div>
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